Neighbourhood and Lattice Models of Second-Order Intuitionistic Propositional Logic

We study a version of the Stone duality between the Alexandrov spaces and the completely distributive algebraic lattices. This enables us to present lattice-theoretical models of second-order intuitionistic propositional logic which correlates with the Kripke models introduced by Sobolev. This can be regarded as a second-order extension of the well-known correspondence between Heyting algebras and Kripke models in the semantics of intuitionistic propositional logic.

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Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).